Cosmology Dr Bryce 29:50 Basic Observations At the beginning of the semester our basic observations were that sky gets dark at night, the Sun rises in the East sets in the West, days are shorter in Winter/longer in summer From these observations we developed our model, the Earth is rotating, the Earth’s rotation axis is tilted Basic Observations When considering the Universe as a whole, what are our basic observation? Stars exist in galaxies and galaxies exist in clusters and clusters exist in super clusters Galaxies are receding from each other The further we look away from the Milky Way the younger the galaxies we see (blue light/low metalicity) and the oldest galaxies are closest to us The oldest stars we see are about 12 billion years old The standard model When we put these observations together we come up with the standard model The Universe is expanding The Universe had a “starting” point (i.e. the Universe has a finite age) The laws of physics are the same everywhere in the Universe The Universe is all made of the same matter (stars, gas, dust, photons etc) We are not located at a special point in the Universe Olbers’ Paradox If universe were 1) infinite 2) unchanging 3) everywhere the same Then, stars would cover the night sky Night sky is dark because the universe changes with time As we look out in space, we can look back to a time when there were no stars Cosmological Principle On large scales the Universe is both homogeneous and isotropic OR The Universe is the same everywhere Homogeneous: same qualities Isotropic: independent of direction Copernican Principle Named for Nicholas Copernicus (Sun centre-ed solar system) The Earth is not at a central or in anyway special position Quantifying the Universe How many galaxies are in the Universe? What is the typical mass of a Galaxy? Do all galaxies have significant dark matter components? We measure the mass of the solar system using the orbits of planets • Orb. Period • Avg. Distance Or for circles: • Orb. Velocity • Orbital Radius Rotation Possible models for rotation Wheel or Merry-go-round Planetary or Keplerian Milky Way doesn’t rotate like either of these models The visible portion of a galaxy lies deep in the heart of a large halo of dark matter We can measure rotation curves of other spiral galaxies using the Doppler shift of the 21-cm line of atomic H Spiral galaxies all tend to have flat rotation curves indicating large amounts of dark matter Broadening of spectral lines in elliptical galaxies tells us how fast the stars are orbiting These galaxies also have dark matter We can measure the velocities of galaxies in a cluster from their Doppler shifts The mass we find from galaxy motions in a cluster is about 50 times larger than the mass in stars! Clusters contain large amounts of X-ray emitting hot gas Temperature of hot gas (particle motions) tells us cluster mass: 85% dark matter 13% hot gas 2% stars Gravitational lensing, the bending of light rays by gravity, can also tell us a cluster’s mass All three methods of measuring cluster mass indicate similar amounts of dark matter Our Options 1. Dark matter really exists, and we are observing the effects of its gravitational attraction 2. Something is wrong with our understanding of gravity, causing us to mistakenly infer the existence of dark matter Our Options 1. Dark matter really exists, and we are observing the effects of its gravitational attraction 2. Something is wrong with our understanding of gravity, causing us to mistakenly infer the existence of dark matter Because gravity is so well tested, most astronomers prefer option #1 Types of Dark Matter Ordinary Dark Matter (MACHOS) Massive Compact Halo Objects: dead or failed stars in halos of galaxies Extraordinary Dark Matter (WIMPS) Weakly Interacting Massive Particles: mysterious neutrino-like particles MACHOs occasionally make other stars appear brighter through lensing … but not enough lensing events to explain all the dark matter WIMPs There’s not enough ordinary matter, WIMPS are not ordinary matter WIMPs could be left over from Big Bang Models involving WIMPs explain how galaxy formation works Superclusters Superclusters are clusters of clusters Our address becomes Solar System, Milky Way, Local Group, Local Supercluster Region of space about 40 Mega Parsec across and is centred on the Virgo cluster The space between the clusters is empty The Virgo Supercluster Structure beyond the local Supercluster Remember the distribution is three dimensional The superclusters often form “sheets” And there are significant voids Galactic surveys Observe a “slice” of the Universe Show that galaxies occupy strands and sheets The voids may contain dark matter as we are only mapping the light Galactic Surveys Maps of galaxy positions reveal extremely large structures: superclusters and voids Dark matter is still pulling things together After correcting for Hubble’s Law, we can see that galaxies are flowing toward the densest regions of space Time in billions of years 0.5 2.2 5.9 8.6 13.7 13 35 70 93 140 Size of expanding box in millions of light-years Models show that gravity of dark matter pulls mass into denser regions – universe grows lumpier with time Structures in galaxy maps look very similar to the ones found in models in which dark matter is WIMPs Contents of Universe “Normal” Matter: ~ 4.4% Normal Matter inside stars: ~ 0.6% Normal Matter outside stars: ~ 3.8% Dark Matter: ~ 25% Dark Energy ~ 70% Unseen Influences Dark Matter: An undetected form of mass that emits little or no light but whose existence we infer from its gravitational influence Dark Energy: An unknown form of energy that seems to be the source of a repulsive force causing the expansion of the universe to accelerate The expansion age Expansion implies that there was a time at which everything was close together From the exapansion rate we can calculate the amount of time the Universe has been expanding If you have driven 180 miles at 60 mph, how long have you been driving for 1 t H Assumes that the expansion rate of the Universe doesn’t change Called the Hubble time Large values of H give us a young Hubble time and small values give us old Hubble time For example if early expansion happened at a slower rate than we observe currently the age of the Universe will be older than the Hubble time General relativity General relativity describes the behaviour of spacetime in the presence of matter General relativity gives us the mathematical tools required to study the Universe “Field Equations” Allows us to develop cosmological models in which we consider the properties of space Is spacetime curved or flat? Positive Curvature Positive Curvature Living on the surface of the Earth it is hard to detect that the Earth is curved The surface of the Earth is finite Likewise if the Universe has positive curvature it would be finite in extent There are no boundaries There is no centre to the surface, no unique points on the surface of a sphere Flat space Flat Space The easiest option for us to visualize Familiar geometric properties 2-dimensional flat space has infinite area and could contain infinite mass There are no boundaries There is no centre Negative curvature Negative Curvature Saddle shaped Has infinite area and can have infinite mass As with flat and positively curved space there are no boundaries There is no centre Testing Curvature Which type of Universe do we live in? What type of geometry matches our observations? What is the circumference of a large circle, the sum of angles in a large triangle? Galaxy counts Instead of “drawing” large circles or triangles we can count the number of galaxies within circles of different radii This assumes that the density of galaxies is uniform on large scales For flat space the number will increase according to pr2, for negatively curved space it will increase more quickly and positively curved space more slowly Complications Galaxies are expanding, the density is changing with time Galaxies change with time causing their luminosities to change, making them more difficult to see Density General relativity tells us the matter (and consequently energy) determines the curvature of spacetime So the density of the Universe is related to the curvature of the Universe A large value of density will give us a positively curved Universe A small value of density will give us a negatively curved Universe Critical density The density of a flat Universe, i.e. the division between positive and negative curvature A slightly denser Universe would be positively curved and slightly less dense would be negatively curved Critical density rc=10-26kg/m3 About 10 hydrogen atoms per cubic meter Critical density parameter Estimates of the density of energy and matter in r the Universe are always compared to the critical o density Astronomers use this ratio If less than 1 negative curvature rc If more than 1 positive curvature What makes up the density All normal matter, us, stars, gas, dust All photons All neutrinos Dark matter Forms of energy that we do not yet know of The role of expansion If the Universe is made up of the matter and energy we can see and infer, then expansion is slowing down because of the gravitational pull of the Universe itself. Consider throwing a ball up and down… The escape velocity is the velocity with which the ball can escape from Earth’s gravitational field Does the universe have enough kinetic energy to escape its own gravitational pull? This depends on the rate of expansion (the Hubble constant) and the average density of the Universe A slow expansion and high density will result in a Universe that will reach a maximum size stop expanding and start contracting A fast expansion and low density will result in a Universe that will expand forever Expansion scenarios Fate of universe depends on the amount of dark matter Critical Lots of Not enough density of dark matter dark matter matter Amount of dark matter is ~25% of the critical density suggesting fate is eternal expansion Not enough dark matter But expansion appears to be speeding up! Dark Not enough Energy? dark matter Dark Energy Energy associated with the acceleration of the expansion rate Einstein included a “cosmological constant” in his famous field equations to allow a static solution. Matter slows expansion whereas dark energy accelerates expansion Fig.26.12 As the density of the Universe decreases the dominant force changes from matter to dark energy old older oldest Estimated age depends on both dark matter and dark energy Brightness of distant white-dwarf supernovae tells us how much universe has expanded since they exploded Accelerating universe is best fit to supernova data Results Distant supernova are brighter than their redshift suggests, i.e. expansion was slower in the past Universe is very close to being flat with 27% of the density supplied by normal mass and energy and 73% supplied by dark energy The Hubble constant is 70km/s per Mpc The age of the Universe is 13.7 billion year The early universe must have been extremely hot and dense Photons converted into particle-antiparticle pairs and vice-versa E = mc2 Early universe was full of particles and radiation because of its high temperature Planck Era Before Planck time (~10-43 sec) No theory of quantum gravity GUT Era Lasts from Planck time (~10-43 sec) to end of GUT force (~10-38 sec) Electroweak Era Lasts from end of GUT force (~10-38 sec) to end of electroweak force (~10-10 sec) Four known forces in universe: Strong Force Electromagnetism Weak Force Gravity Particle Era Amounts of matter and antimatter nearly equal (Roughly 1 extra proton for every 109 proton- antiproton pairs!) Era of Nucleo- synthesis Begins when matter annihilates remaining antimatter at ~ 0.001 sec Nuclei begin to fuse Era of Nuclei Helium nuclei form at age ~ 3 minutes Universe has become too cool to blast helium apart Era of Atoms Atoms form at age ~ 380,000 years Background radiation released Era of Galaxies Galaxies form at age ~ 1 billion years Primary Evidence 1) We have detected the leftover radiation from the Big Bang. 2) The Big Bang theory correctly predicts the abundance of helium and other light elements. The cosmic microwave background – the radiation left over from the Big Bang – was detected by Penzias & Wilson in 1965 Background radiation from Big Bang has been freely streaming across universe since atoms formed at temperature ~ 3,000 K: visible/IR Before and After recombination Small fluctuations in the CMB Background has perfect thermal radiation spectrum at temperature 2.73 K Expansion of universe has redshifted thermal radiation from that time to ~1000 times longer wavelength: microwaves Cosmic Microwave Background Close to perfect blackbody spectrum Temperature of 2.725K Same temperature in every direction Temperature variations are very very small ~0.0001K CMB is the surface of last scattering Oldest object we can observe Protons and neutrons combined to make long- lasting helium nuclei when universe was ~ 3 minutes old Big Bang theory prediction: 75% H, 25% He (by mass) Matches observations of nearly primordial gases Inflation addresses three issues 1) Where does structure come from? 2) Why is the overall distribution of matter so uniform? 3) Why is the density of the universe so close to the critical density? Inflation can make all the structure by stretching tiny quantum ripples to enormous size These ripples in density then become the seeds for all structures How can microwave temperature be nearly identical on opposite sides of the sky? Regions now on opposite sides of the sky were close together before inflation pushed them far apart Overall geometry of Density = Critical the universe is closely related to total density of matter & energy Density > Critical Density < Critical Inflation of universe flattens overall geometry like the inflation of a balloon, causing overall density of matter plus energy to be very close to critical density Inflation Patterns of structure observed by WMAP show us the “seeds” of universe Observed patterns of structure in universe agree (so far) with the “seeds” that inflation would produce “Seeds” Inferred from CMB • Overall geometry is flat – Total mass+energy has critical density • Ordinary matter ~ 4.4% of total • Total matter is ~ 27% of total – Dark matter is ~ 23% of total – Dark energy is ~ 73% of total • Age of 13.7 billion years Dark Matter Matter that doesn’t reflect or emit light Inferred from gravitational interactions Is important for structure formation Contemporary evidence suggests that dark matter is most likely new elementary particles (often called non baryonic dark matter) Dark Energy Hypothetical form of energy that produces an acceleration in the rate of expansion of the Universe Presence of Dark Energy is also indicated by measurements of the cosmic microwave background, gravitational lenses and the large scale structure of the Universe Non standard Models Steady State Universe; the Universe is infinite in extent and relatively unchanging. It cannot explain the presence of the cosmic microwave background Non standard models Tired light; instead of the observed redshifts being due to expansion they are due to the photons losing energy on the journey to us. Incorrect as the light we see isn’t blurred and the physical processes by which the photons would lose energy would cause blurring Philosophical points Omphalos; the idea that the Universe was made to look old in order to be functional, completely unverifiable and unfalsifiable. NOT a scientific theory Fine tuning Small changes in physical constants such as G would have a huge impact on the Universe, for example whether or not stars could shine. The conditions that allow life depend on these constants being correct. Counterargument is that many failed Universes could have existed. Again not testable. Anthropic Principle We must remember that we can only observe our Universe because we are in it! The existence of multiple universes or a designer are highly controversial and as these ideas are un-testable this means that they outside the realms of science, no matter how interesting they may be philosophically.